The amount of money collected by a snack bar at a large university has been recorded daily for the past fiveyears. Records indicate that the mean daily amount collected is $4000 and the standard deviation is $450. Thedistribution is skewed to the right due to several high volume days (including football game days). Supposethat 100 days were randomly selected from the five years and the average amount collected from those dayswas recorded. Which of the following describes the sampling distribution of the sample mean?
A) normally distributed with a mean of $4000 and a standard deviation of $45
B) normally distributed with a mean of $4000 and a standard deviation of $450
C) normally distributed with a mean of $400 and a standard deviation of $45
D) skewed to the right with a mean of $4000 and a standard deviation of $450

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean will be approximately normally distributed due to the Central Limit Theorem, which applies because the sample size is large (n=100). The mean of the sampling distribution is equal to the population mean ($4000), and the standard deviation of the sampling distribution (standard error) is the population standard deviation ($450) divided by the square root of the sample size (√100), which equals $45.

The Amount of Money Collected by a Snack Bar at a Large